Bare phosphor-coated lighting-emitting diodes (i.e., unencapsulated light-emitting diode (LED) die with a conformal phosphor coating) typically exhibit a Lambertian luminous intensity distribution that is described by:I(θ)=In×cos(θ)where In is the intensity measured perpendicular to the light-emitting surface and I(θ) is the intensity measured at angle θ from the surface normal. A schematic luminous intensity plot of such a Lambertian emitter is shown in FIG. 1, where the light source is located at the center of the large sphere and points on the smaller sphere represent the intensity plot—i.e., the intensity value as a function of angle from the normal. As shown in the figure, the apparent brightness to an observer is the same regardless of the observer's angle of view.
For many lighting applications, however, it is desirable for luminaires to have a luminous intensity distribution such that the illuminance of the workplane below the luminaire or the ceiling above the luminaire is substantially constant. For an infinite linear source, the illuminance E of a plane parallel to and at a distance dn from the light source is given by:E(θ)=I(θ)×cos2(θ)/dn where θ is the angle in the direction perpendicular to the linear light source. To maintain spatially constant illuminance with a linear light source, it is therefore necessary that:I(θ)=In/cos2(θ)in the direction perpendicular to the light source axis.
Again, however, for architectural applications, and in particular for office lighting, luminaires with linear fluorescent lamps are typically arranged in parallel rows such that their luminous intensity distributions overlap. As such, a more desirable intensity distribution is:I(θ)=/cos(θ)
Luminaires designed for office lighting applications generally also comply with the recommendations of ANSI/IES RP-1, Office Lighting, which limits the luminous intensity at oblique viewing angles. A theoretical luminous intensity distribution satisfying these requirements over the range −30°<0<30° is shown in FIG. 2. One attempt to realize this distribution is the direct-indirect linear fluorescent luminaire (Model 7306T02IN as manufactured by Ledalite, Langley, BC, Canada), the measured luminous intensity distribution of which is shown in FIG. 3A (viewed perpendicular to the lamp axis) and FIG. 3B (viewed parallel to the lamp axis).
The downward component illustrated in FIG. 3A exhibits a distribution similar to that of FIG. 2, while the downward component of FIG. 3B exhibits a substantially Lambertian distribution similar to FIG. 1. The latter distribution is a consequence of the fact that four-foot fluorescent lamps are essentially linear light sources, so the luminous intensity distribution in the direction parallel to the lamp axis cannot be controlled without substantial light losses, and also need not satisfy the inverse cosine relationship: the continuous distribution of light along the length of the luminaires will tend to provide constant illuminance on the workplane or ceiling in the same direction. However, the recommendations of ANSI/IES RP-1 must still be satisfied for many commercial applications.
For illuminated ceilings in open-plan offices, ANSI/IES RP-1, Office Lighting, also recommends a brightness uniformity ratio of 8:1 or less, and preferably 4:1 or even 2:1 if possible. This is typically accomplished with linear fluorescent luminaires having a so-called “batwing” luminous intensity distribution, such as is exhibited, for example, by the upward component of the luminous intensity distribution shown in FIGS. 3A and 3B. The ideal batwing distribution is similar to FIG. 2, but with a wider range. Assuming a typical suspension distance of 16 inches below the ceiling and a luminaire row operation of 6 feet, the range of constant illuminance should be at least −65°<θ<65°. Another approach is to optically couple high-power LED packages with external optics. The resulting distribution, however, may be too collimated for most architectural lighting applications, and the optical assembly too large for most luminaire designs.
There are in addition applications requiring an asymmetric luminous intensity distribution. As one example, linear fluorescent luminaires are often mounted on walls near the ceiling of a room as “cove lighting” to provide substantially constant illumination of the wall surface, typically with the use of physically large asymmetric reflectors.
There is, therefore, a need for a monolithic optical lens design that can generate a luminous intensity distribution from an array of light-emitting elements to provide spatially constant illumination of a surface, such as a workplane, ceiling or wall, and in a form factor that is compatible with the optical, mechanical and aesthetic design requirements of luminaires intended for architectural applications such as office lighting.